The 1889 Regulation of Railways Act states that a passenger must on request surrender either:
1) A ticket for the journey
2) The fare for the journey
or
3) The persons name and address.
If a person fails to do any of the three, then a Railway Employee may arrest without warrant that person - they will have then committed an offence which should be dealt with by way of summons (or s.25 PACE arrest if they persist in refusing to give details).
Should they offer their name and address, then the train company will bill them for the fare. Non payment then is generally dealt with as a civil matter.
If someone has faked a ticket, then they can be arrested for attempting to obtain a service by deception.